Bending a pole with wind
Final result:



It's animated wind with changing strength.

Steps:


Create Cylinder with only 6 vertices and some small radius (for me it's 5cm).
Go to Edit Mode and add 3 Loop Cuts.
Select bottom Edge Loops and add them to Vertex Group.





Exit Edit Mode and add Soft Body physics to our cylinder.
First set the Goal Strength to 1 and as Vertex Group select the one we created before.
Add some wind to test it out.
Go to Soft Body Edges tab and Soft Body Self Collision and make changes accordingly to picture below.





That's it.


Final thoughts:

If you want it to look smooth, add Edge Creases 1 to top and bottom edge loop, select Shading Smooth, turn on Auto Smooth and add Subdivision Surface modifier.

Note. Settings may differ accordingly to edge loops count, pole length and such.
You will want to tweak then such values as Pull, Push and Bending.

Note 2. To control jiggling and bending strength change Soft Body Mass.

Blend file: